I see it on houses all the time. It'll keep coming back. The sun doesn't shine on the north side so it stays wetter and just like a tree it'll have mold or moss. I have sprayed it with a bleach solution and rinsed it off. If it's bad enough, wash it with the solution and soap and a brush.

I suppose you could work some strands of copper onto the siding to help prevent/slow future growth. I've seen this done on roofs, why not siding? Obviously, it won't get as much exposure as roofing but, it's better than just watching it grow back.